Optical path length measurements, made by interferometry, are highly sensitive and adaptable to the study of a wide range of physical phenomena because they sensitively measure small changes in the optical path length induced by physical process, of the order of a fraction of an optical wavelength.
When a material sample is subjected to a perturbation, any resulting changes in the optical path length to an image plane may be potentially sensed by an interferometer. Optical path length variations occurring along the transverse coordinate of the interferometer may be probed to form an interferometric image: the transverse coordinates of the interferometer are defined as occupying orthogonal directions, (x,y) that lie in the image plane. The primary interferometric image produced by the interferometer is called an interferogram. The interferogram is defined as an image formed by the superposition of two beams of coherent light, I1 and I2, on the image plane of the interferometric imaging system. The interferogram is electronically recorded (such as by a digital camera considered to be a generalized imaging device composed of an array of optical sensing elements (or image pixels) operating over the wavelength range used by the interferometer beams) and the information is stored in a data storing and processing system. The interferogram is commonly referred to as a speckle image (or specklegram s(x,y), speckle image and specklegram are used interchangeably) when a coherent light source is used and the object's surface roughness causes random reflection forming speckles on the image plane. When multiple images are taken, for instance of an object in various stages of deformation, each speckle image is considered a frame.
In speckle pattern interferometry, a speckle image of the object before loading or perturbation (henceforth considered as a “deformation”) is electronically stored. Next a speckle image of the object after deformation is electronically stored. By taking the difference between the speckle images before and after deformation it is possible to observe a speckle interference fringe pattern. The interference pattern appears as dark and light regions which show the deformation distribution. Hence, interferometry can be used to determine the response of a material to a load or deformation, but it is not particularly useful in analyzing or characterizing the type or degree of deformation of the object or medium, such as elastic deformation, plastic deformation or deformation near the fracture point. Indeed, a fracture generally cannot be predicted until a crack is found in the object. It is not easy to find a crack in its early stage, and in some cases the crack is too large or the fracture point reached when it is found.
What is needed is a technique that enables the diagnosis of the current degree of deformation, to allow prediction on the progress of the deformation, and to predict the location where the material may eventually fracture, without relying on the existence of a crack.
One attempt to formalize a theory of deformation that describes all the stages of deformation inclusively is mesomechanics, developed by Panin et al. [1] V. E. Panin, Ed., Physical Mesomechanics of Heterogeneous Media and Computer-Aided Design of Materials, vol.1, Cambridge International, Cambridge, England, 1998 (hereby incorporated by reference). According to this theory, the displacement field of a plastically deforming object is governed by relationships similar to the Maxwell equations for an electromagnet field. Mesomechanics has derived the following relationships:div{right arrow over (V)}=ρ/ε  (1)div{right arrow over (Ω)}=0  (2)
                              curl          ⁢                      V            →                          =                              ∂                          Ω              →                                            ∂            t                                              (        3        )                                          curl          ⁢                      Ω            →                          =                                            -                              (                                  1                  /                                      c                    2                                                  )                                      ⁢                                          ∂                                  V                  →                                                            ∂                t                                              -                      J            →                                              (        4        )            where {right arrow over (V)}, {right arrow over (Ω)} and {right arrow over (J)} are vectors,    {right arrow over (V)}=rate of displacement vector (a velocity vector)    {right arrow over (Ω)} =rotation or curl of the displacement (it can be defined by equation (3))    {right arrow over (J)}/μ=a quantity that is analogous to the electric current density, where μ is a material dependent constant,    c=1/(εμ)1/2=the phase velocity of the transverse displacement wave where ε=density, 1/μ effective stiffness of shear force    ρ=a quantity analogous to electric charge densityDivergence of eq. (4) leads to an equation analogous to the charge conservation law or the continuity equation:0=−1/c2∂{right arrow over (V)}/∂t−div({right arrow over (J)}) (using equation 1 substitute div{right arrow over (V)}) or div({right arrow over (J)}/μ)=−∂(εdiv {right arrow over (V)})/∂t=−∂ρ/∂t  (5)Equation (4) can also be expressed as
                              curl          ⁢                      Ω            →                    ⁢                      /                    ⁢          μ                =                                            -              ɛ                        ⁢                                          ∂                                  V                  →                                                            ∂                t                                              -                                    J              →                        μ                                              (                  4          ′                )            Where −{right arrow over (J)}/μ represents the longitudinal force and −(1/μ)curl{right arrow over (Ω)} represents the shear force, as explained later.
While mesomechanical theory provides a formalism for deformation theory, the correspondence of the theory's variables to observational data or the conventional theory of elasticity has been lacking. One attempt to develop a formal approach using mesomechanics is that shown in U.S. Pat. No. 5,508,9801 to Panin. This patent, using a mesomechanical theory for interpretation of deformation, utilizes a double exposed hologram to calculate certain velocity tensor parameters. However, Panin does not specify what mesomechanical conditions should be used to predict the evolution of the deformation to fracture and the Panin technique uses a very awkward system to produce the mesomechanical fields.
Panin records a single holograph having a double recorded image (time 1 and time 2). The resultant fringe patterns are displayed by projecting onto a screen. The screen pattern is analyzed to determine the velocity vector field. The Panin technique but uses a multiplier (s/d) applied to the phase component, which is determined by direct measurement from the hologram image displayed by holographic projection onto a screen. Measurements must be undertaken by hand.